Practice songs with your hand on your chest to ensure that you are using the proper technique as your chest will move in and out as you sing. Start with simple songs that you know you can sing and slowly incorporate songs that are more difficult for you. Continue to sing them until you start to hear improvements, as practice is the only way to get better and improve your range.
Sing along with songs using your head voice, or falsetto. Keep your hand on your chest and make sure that it does not move during these exercises. Start with some easy tunes that incorporate this style and work your way up to harder passages that may initially strain your voice, but keep at it for improvement. Since the head voice is in an already very high register, these exercises will increase your range in the upper registers.
Perform scales using your chest voice, which is usually your strongest singing voice. Start at a moderately low note and sing a major scale, including all of the notes up to and including the octave. Move on to the next note and sing the scale and octave as well. Continue this until you are out of your comfort zone. Over time, you should be able to sing higher and extend your range without cracking or running out of breath.
Perform the scales as well as the octaves using your head voice. Your head voice is also your falsetto voice and is used for higher notes. Start at your lowest head voice note and work your way up until you can no longer sing that higher. Over time, you will expand your head voice and your overall range and singing will be stronger.
Work on exercises that bridge the gap between your head and chest voices. While many singers are good at one or the other, bridging them seamlessly will improve your range. Professional singers who have multi-octave ranges are able to seamlessly move from their chest voice to their head voice. Exercises including the grunting technique -- which quickly takes you from a grunt to a much higher note -- condition your voice to go from your chest to head voices with ease.